{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5929387a-0224-48f3-a92e-1114647c06ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "softmax回归算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b4b0a5ca-1cf8-4d3b-8897-c5369d8fa95c",
   "metadata": {},
   "outputs": [],
   "source": [
    "   模型输出可以是⼀个像图像类别这样的离散值。对于这样的离散值预测问题，我们可以使⽤诸如softmax回归在内的分类模型。\n",
    "softmax回归的输出单元从⼀个变成了多个，且引⼊了softmax运算使输出更适合离散值的预测和训练。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6bbeed9b-c76d-421b-a7d3-8c00f81f9bd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "   我们通常使⽤离散的数值来表示类别，例如 。如此，⼀张图像的标签为1、2和3\n",
    "这3个数值中的⼀个。虽然我们仍然可以使⽤回归模型来进⾏建模，并将预测值就近定点化到1、2和3\n",
    "这3个离散值之⼀，但这种连续值到离散值的转化通常会影响到分类质量。因此我们⼀般使⽤更加适合\n",
    "离散值输出的模型来解决分类问题。\n",
    "    softmax回归的输出值个数等于标签⾥的类别数。因为⼀共有4种特征和3种输出动物类别，所以权重包\n",
    "含12个标量、偏差包含3个标量，且对每个输⼊计算 这3个输出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0f42c68c-98f5-419d-9cdd-ce0e14fe798b",
   "metadata": {},
   "outputs": [],
   "source": [
    "运用softmax运算符（softmax operator）解决⼀⽅⾯，由于输出层的输出值的范围不确定，我们难以直观\n",
    "上判断这些值的意义。例如，刚才举的例⼦中的输出值10表示“很置信”图像类别为猫，因为该输出值是\n",
    "其他两类的输出值的100倍。但如果 ，那么输出值10却⼜表示图像类别为猫的概率很\n",
    "低。另⼀⽅⾯，由于真实标签是离散值，这些离散值与不确定范围的输出值之间的误差难以衡量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "599930af-85b8-4328-8d40-6a3397b7c7f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "交叉熵损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "35a7ca8b-90d5-48b2-8dd0-251bded83bdf",
   "metadata": {},
   "outputs": [],
   "source": [
    "想要预测分类结果正确，我们其实并不需要预测概率完全等于标签概率\n",
    "应该⽤更适合衡量两个概率分布差异的测量函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "91d33010-cdb1-46b6-a44e-c5cc31eab44d",
   "metadata": {},
   "outputs": [],
   "source": [
    "输出类别是预测概率最⼤的类别。如果它与真实类别（标签）⼀致，说明这次预测是正确的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "54c0a485-86d5-4b65-8dbe-079e862ce125",
   "metadata": {},
   "outputs": [],
   "source": [
    "我们将使⽤torchvision包，它是服务于PyTorch深度学习框架的，主要⽤来构建计算机视觉模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a1b65f38-13ff-4e4e-b2f3-9b9b8e1d8179",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import sys\n",
    "import sys\n",
    "import os\n",
    "sys.path.append(\"..\") # 为了导⼊上层⽬录的d2lzh_pytorch\n",
    "import d2lzh_pytorch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05372db0-0310-4bc3-a4fb-29efca3bb191",
   "metadata": {},
   "outputs": [],
   "source": [
    "我们还指定了参数 transform = transforms.ToTensor() 使所有数据转换为 Tensor ，如果不\n",
    "进⾏转换则返回的是PIL图⽚。 transforms.ToTensor() 将尺⼨为 (H x W x C) 且数据位于[0, 255]的\n",
    "PIL 图 ⽚ 或 者 数 据 类 型 为 np.uint8 的 NumPy 数 组 转 换 为 尺 ⼨ 为 (C x H x W) 且 数 据 类 型\n",
    "为 torch.float32 且位于[0.0, 1.0]的 Tensor 。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7043de1f-03f7-4490-96f7-d92c2932aa6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "mnist_train = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', \n",
    "train=True, download=True, transform=transforms.ToTensor())\n",
    "mnist_test = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', \n",
    "train=False, download=True, transform=transforms.ToTensor())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "095d8fd9-684e-4ffb-8b0e-c3fec8c6187b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'torchvision.datasets.mnist.FashionMNIST'>\n",
      "60000 10000\n"
     ]
    }
   ],
   "source": [
    "print(type(mnist_train))\n",
    "print(len(mnist_train), len(mnist_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a79cee37-86f5-4811-8b9b-602831771048",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 28, 28]) 9\n"
     ]
    }
   ],
   "source": [
    "feature, label = mnist_train[0]\n",
    "print(feature.shape, label) # Channel x Height X Width"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8fbe439e-cd55-4e73-a3a8-24825b92053e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_fashion_mnist(images, labels):\n",
    "    d2l.use_svg_display()\n",
    "    # 这⾥的_表示我们忽略（不使⽤）的变量\n",
    "    _, figs = plt.subplots(1, len(images), figsize=(12, 12))\n",
    "    for f, img, lbl in zip(figs, images, labels):\n",
    "        f.imshow(img.view((28, 28)).numpy())\n",
    "        f.set_title(lbl)\n",
    "        f.axes.get_xaxis().set_visible(False)\n",
    "        f.axes.get_yaxis().set_visible(False)\n",
    "    plt.show()\n",
    "#将数值标签转换为文本标签\n",
    "def get_fashion_mnist_labels(labels):\n",
    "    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat','sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']\n",
    "    return [text_labels[int(i)] for i in labels]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "594b9ab6-254c-4e94-8c46-c9d806074183",
   "metadata": {},
   "outputs": [
    {
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       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 1200x1200 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = [], []\n",
    "for i in range(10):\n",
    "    X.append(mnist_train[i][0])\n",
    "    y.append(mnist_train[i][1])\n",
    "show_fashion_mnist(X,get_fashion_mnist_labels(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73e52031-eb57-4166-b9d5-29457275ab37",
   "metadata": {},
   "outputs": [],
   "source": [
    "在实践中，数据读取经常是训练的性能瓶颈，特别当模型较简单或者计算硬件性能较⾼时。PyTorch的\n",
    "DataLoader 中 ⼀ 个 很 ⽅ 便 的 功 能 是 允 许 使 ⽤ 多 进 程 来 加 速 数 据 读 取 。 这 ⾥ 我 们 通 过 参\n",
    "数 num_workers 来设置4个进程读取数据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "32967671-ff38-4e7b-8c77-1d1f953441b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 256\n",
    "if sys.platform.startswith('win'):\n",
    "    #在win上避免由于多线程带来的影响\n",
    "    num_workers = 0 # 0表示不⽤额外的进程来加速读取数据\n",
    "else:\n",
    "    #mac和linux可以使用多线程进行操作\n",
    "    num_workers = 4\n",
    "train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)\n",
    "test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74d93698-9f42-4fbe-8d9d-a1b588d40314",
   "metadata": {},
   "outputs": [],
   "source": [
    "查看训练需要的时间"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "33c7bf1d-f193-4ab4-b402-46efa2d5a0cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.38 sec\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "for X, y in train_iter:\n",
    "    continue\n",
    "print('%.2f sec' % (time.time() - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec305447-4c06-4f95-88f9-633c789938c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "SOFTMAX回归的从零开始实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "dd80bcce-4af4-4065-8dd9-602efddeb815",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torchvision\n",
    "import numpy as np\n",
    "import sys\n",
    "sys.path.append(\"..\") # 为了导⼊上层⽬录的d2lzh_pytorch\n",
    "import d2lzh_pytorch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0fb20283-2974-4abe-9e43-d340890d6542",
   "metadata": {},
   "outputs": [],
   "source": [
    "我们将使⽤Fashion-MNIST数据集，并设置批量⼤⼩为256。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3fee489-f7b4-499d-be8c-0b1477d24ff1",
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 256\n",
    "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c776e70-39cf-4392-8842-0147d0e3fd0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "跟线性回归中的例⼦⼀样，我们将使⽤向量表示每个样本。已知每个样本输⼊是⾼和宽均为28像素的图\n",
    "像。模型的输⼊向量的⻓度是 ：该向量的每个元素对应图像中每个像素。由于图像有\n",
    "10个类别，单层神经⽹络输出层的输出个数为10，因此softmax回归的权重和偏差参数分别为794*10\n",
    "和1*10的矩阵。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "830a1fe0-059e-4d9a-a159-ee5af678c030",
   "metadata": {},
   "outputs": [],
   "source": [
    "#28*28像素点得到784个数据输入\n",
    "num_inputs = 784\n",
    "num_outputs = 10\n",
    "W = torch.tensor(np.random.normal(0, 0.01, (num_inputs, num_outputs)), dtype=torch.float)\n",
    "b = torch.zeros(num_outputs, dtype=torch.float)\n",
    "#求模型的参数梯度\n",
    "W.requires_grad_(requires_grad=True)\n",
    "b.requires_grad_(requires_grad=True) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "46eaeaed-ec90-493f-a747-4adace52a177",
   "metadata": {},
   "outputs": [],
   "source": [
    "实现SOFTMAX运算\n",
    "给定⼀个 Tensor 矩阵 X 。我们可以只对其中同⼀列（ dim=0 ）或同⼀⾏（ dim=1 ）的元素求\n",
    "和，并在结果中保留⾏和列这两个维度（ keepdim=True ）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "51b930b5-31ef-4b9e-823b-d11ceeb918f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "不同维度求和算法\n",
    "X = torch.tensor([[1, 2, 3], [4, 5, 6]])\n",
    "print(X.sum(dim=0, keepdim=True))\n",
    "print(X.sum(dim=1, keepdim=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47242fbb-1633-4edb-a61d-b908c7bf6083",
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(X):\n",
    "    X_exp = X.exp()    #这里使得每个数的特征更加明显，同时保证为非负数\n",
    "    partition = X_exp.sum(dim=1, keepdim=True)\n",
    "    return X_exp / partition # 这⾥应⽤了⼴播机制"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92129881-5d8e-4468-a6a8-65cca13945e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "定义softmax回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5daafa7a-a23a-4935-8834-c0a2ab322af3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def net(X):\n",
    "    return softmax(torch.mm(X.view((-1, num_inputs)), W) + b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2824b82d-6948-4f5b-b444-d1726bca5259",
   "metadata": {},
   "outputs": [],
   "source": [
    "定义交叉熵损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b778b96-0a14-4f87-aa21-6a4d03ce1fee",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cross_entropy(y_hat, y):\n",
    "    return - torch.log(y_hat.gather(1, y.view(-1, 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d3720a0-44ed-4aef-aa8d-9c4b59585f3f",
   "metadata": {},
   "outputs": [],
   "source": [
    "计算分类的准确率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5c090f27-1194-4984-90ff-ab671c1560ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(y_hat, y):\n",
    "    return (y_hat.argmax(dim=1) == y).float().mean().item()"
   ]
  }
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